From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3813 Path: news.gmane.org!not-for-mail From: Steven R. Costenoble Newsgroups: gmane.science.mathematics.categories Subject: Maps of monads - references Date: Tue, 10 Jul 2007 09:25:28 -0400 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 (Apple Message framework v752.3) Content-Type: text/plain; charset=US-ASCII; delsp=yes; format=flowed Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241019539 10401 80.91.229.2 (29 Apr 2009 15:38:59 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:38:59 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Tue Jul 10 14:42:08 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 10 Jul 2007 14:42:08 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1I8JeF-0003Y1-8n for categories-list@mta.ca; Tue, 10 Jul 2007 14:37:15 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 7 Original-Lines: 20 Xref: news.gmane.org gmane.science.mathematics.categories:3813 Archived-At: In Toposes, Triples, and Theories, Barr and Wells define a morphism of triples (which, being a student of Peter May, I will call a map of monads) in the context of two monads on a given category C. I have a situation where I have two categories C and D, a monad S on C, a monad T on D, and a functor F: C -> D. There is a fairly obvious generalization of the TTT definition, to say that a map from S to T is a natural transformation FS -> TF making certain diagrams commute. My guess is that someone else noticed this long ago, so I'm looking for references to where this has appeared in the literature. I'm particularly interested in references that include the fact (at least, I'm pretty sure it's a fact) that such maps are in one-to-one correspondence with extensions of F to a functor between the respective Kleisli categories of S and T. Thanks in advance. --Steve Costenoble